What is the extraneous solution to these equations? $\dfrac{x^2}{x - 7} = \dfrac{100}{x - 7}$
Solution: Multiply both sides by $x - 7$ $ \dfrac{x^2}{x - 7} (x - 7) = \dfrac{100}{x - 7} (x - 7)$ $ x^2 = 100$ Subtract $100$ from both sides: $ x^2 - (100) = 100 - (100)$ $ x^2 - 100 = 0$ Factor the expression: $ (x + 10)(x - 10) = 0$ Therefore $x = -10$ or $x = 10$ The original expression is defined at $x = -10$ and $x = 10$, so there are no extraneous solutions.